Conventional laterally guided vehicles rely on lateral guide rails to stabilize and direct them along the guideway. In one approach this is done with lateral rollers that engage the lateral rails and continuously hunt from side to side resulting in lateral bounce and uncomfortable "head toss". This occurs because the lateral rollers on each side are fixed together in a four bar linkage so that any bump in a guide rail will be translated from the associated lateral guide roller to the entire mechanism and steer the castered support tires to move the vehicle in the other direction from the bump. Thus the vehicle is urged toward the other guide rail. As a result the vehicle swings from side to side causing noise, head toss and other passenger discomfort and wear and damage to the vehicle. In another approach, in order to avoid the head-toss problem the support tires are constantly steered toward one or the other of the guide rails causing scrubbing of the tires and premature wear. In addition, the force of friction between the tires and their footprint on the guideway is a significant distance from the center of gravity of the vehicle, causing annoying and dangerous roll forces on the passenger and vehicle. In such approaches the wide range and unpredictability of movement of the guide wheels and the vehicle as a whole require wider guideways and greater tolerances for power collection and communications and makes the lateral wheels' motion unreliable as an indicator of vehicle distance and position.